Particulars: Bundles of Universals?

Overview of the Main Views
on Universals and Particulars

In my view, the "default theory" is realism. That is, there certainly are
individual things and properties of those things. The most obvious position to
take is that the individual things are particulars, their properties are
universals, and both are equally fundamental. If you reject the existence of
universals, you need to find an alternative account of properties; if you reject
the existence of particulars, you need to find an alternative account of
individual things.

So arguments for realism tend to be arguments against the alternative views,
and in particular, arguments that the ways the other views try to define or
account for individual things and properties don't work.

universals are real and
fundamental

universals are not fundamental
(or not real)

Particulars are real
and fundamental

realism

resemblance nominalism
class nominalism
conceptualism

Particulars are not
fundamental (or not real)

bundle theory

trope theory

(Note that Russell is not only a bundle theorist but also a
phenomenalist: he not only wants to define particulars as bundles of universals;
he also wants to define physical things in terms of experiential things. As if
the project wasn't already hard enough!)

The Identity of
Indiscernibles

The Identity of Indiscernibles is one of two principles about identity
associated with Leibniz. The less controversial principle is the
similar-sounding Indiscernibility of Identicals, which simply says that if x and
y are identical (that is, are the same thing), then x has every property
y has and vice versa.

The Identity of Indiscernibles is the converse of this: the view that, if x
and y have all the same properties, then they are identical.

One issue that makes a difference here is exactly what we mean by a
"property." If being identical with Curtis Brown counts as a property, then
clearly it is a property nothing but Curtis Brown can have, and so the Identity
of Indiscernibles becomes trivially true. (Well, it could still be important:
the Indiscernibility of Identicals is an important truth even though it is
similarly trivial.) Similar points arise for the "property" of being different
from Curtis Brown.

But suppose we restrict properties to those that don't depend on particulars.
Then the Identity of Indiscernibles becomes a more interesting doctrine. It may
be an empirical truth, but it doesn't seem to be a necessary truth. Consider
Black's example of the two exactly similar spheres. Doesn't each of the spheres
have all the properties the other one has? They have all the same intrinsic
properties (as long as we are not counting haecceities as intrinsic properties).
And each also seems to have all the relations to the other that the other has to
it. But they are the only two things in the universe, so there is no third thing
for them to have different relations to.

The one sticking point may be spatial properties. The spheres occupy
different locations. But it seems that this can only distinguish them if
locations are themselves particulars. Then At(x, l) is a relation between an
object and a location. But we agreed not to count relations to particulars as
properties, so relations to particular locations would seem to be ruled out as
well. The only spatial properties that will be legitimate are relational
properties, e.g. being 50 meters from a steel sphere. And the two spheres have
all the same properties of this sort.

[Unless they can be distinguished by their modal properties: there could be
an object further from a than from b.

The "Bundle Theory" of
Particulars

The Bundle Theory says that particulars can be "reduced" to universals.
Ultimately all that exists is universals; when we talk about particulars, we are
really talking about universals.

One version of this view is the idea that a particular is a set of
universals. van Cleve offers six objections to this view, of which the last
three also apply to some of the more sophisticated versions of the view.

The sixth objection is that if the bundle theory were true, then the identity
of indiscernibles would be a necessary truth. As we've seen above, it doesn't in
fact seem to be a necessary truth. So the bundle theory must be false.

Summary of the Argument
Against the Bundle Theory

1. If the bundle theory is correct, then the identity of indiscernibles
is a necessary truth.
2. If the identity of indiscernibles is a necessary truth, then there cannot
be two distinct objects with exactly the same properties.
3. The example of the two spheres shows that there could be two distinct
objects with exactly the same properties.
Therefore,
4. The bundle theory is not correct.